Proportionalities

1
Proportionalities
B
w
D
A
z
x
y
C

• A/w
• A/x
• B/x
• C/x
• D/x
• D/w

A z

?
2
Proportionalities
B
D
F
E
A
C

• E/F
• F/E
• D/F
• F/D
• E/D
• D/E

A C

?
3
Proportionalities
r
R
A
a

• R-r
• Rr
• R2/r2
• R2/r
• R/r
• r/R

A a

?
4
Proportionalities
r
R
a
A

• ?R/r
• R/?r
• R2/r2
• ?R2/r
• R/r
• r2/R2

A a

?
5
The same proportionalities work for arc-lengths
r
R
s
S
S R s r

area at S R2 area at s r2

6
The electric field at the very CENTER of this
spherical conductor

• points out
• points in
• points up
• points left
• points right
• points down
• is zero

E ?




















7
What is the electric field at the very CENTER
of this spherical conductor?













E 0!!









8
The electric field at this off-CENTER
point within the spherical conductor

• points out
• points in
• points up
• points left
• points right
• points down
• is zero

E ?




















9
Gauss Law
FLUX E ? A
FLUX flow number of lines entering or leaving
a region (volume)
10
If more lines exit than enter denotes a
concentration of positive charge within
If more lines enter than leave denotes a
concentration of negative charge within
11
(No Transcript)
12
A cube with edge, L, and surface area A on each
face, is immersed in a uniform electric field
E as shown.

• EA
• - EA
• EL
• - EL
• 0

The flux through its bottom surface is
13
A cube with edge, L, and surface area A on each
face, is immersed in a uniform electric field
E as shown.

• EA
• - EA
• EL
• - EL
• 0

The flux through its top surface is
14
A cube with edge, L, and surface area A on each
face, is immersed in a uniform electric field
E as shown.

• EA
• - EA
• EL
• - EL
• 0

The flux through its front-facing surface is
15
A cube with edge, L, and surface area A on each
face, is immersed in a uniform electric field
E as shown.
The total flux through this cube is

• 2EA
• - 2EA
• 6EL
• - 4EL
• 0

16
Gaussian Surfaces
17
Electron Gun
Heated filament
Positively charged can
If the effective field is E800,000 N/C over a
gap length of 2.5 cm, what is the electrons
final velocity, v?